Charting a sustainable tomorrow: Advancing urban low-carbon economies through comprehensive evaluation and promotion

With the world population growth, energy consumption and the rapid development of industrial economy, a large amount of carbon emissions has brought destruction and threats to the earth’s environment on which human beings depend. The development of low-carbon economy has become the consensus of governments all over the world and has been vigorously advocated & promoted. This paper focuses on the top five global GDP nations in 2022: The United States, China, Japan, Germany, and Britain. A comprehensive evaluation index system of urban low-carbon economic development level is constructed from four dimensions: economic development level, environmental quality, energy consumption emission intensity and social development speed by using literature review and field interview. The evaluation measures are determined using the TOPSIS evaluation method with entropy weight and the grey relational model, providing a comprehensive assessment of the low-carbon economy’s development level in these five countries." Judging from the comprehensive evaluation score, the overall development of low-carbon economy in American cities is in good condition and has reached the development standard of low-carbon economy; Germany and Japan rank second and third, and they are low-carbon economies. Britain ranks fourth in comprehensive evaluation, although it belongs to a low-carbon economy country, but there is still a certain gap with Germany and Japan; There is still a big gap between China and the other four countries. Based on the measurement and evaluation outcomes, it presents recommendations and strategies to foster the growth of low-carbon economies, offering valuable insights for the advancement of such economies across different nations. The research results guide countries all over the world to reduce carbon emissions in the process of economic development, protect the earth environment on which human beings depend, and make a better tomorrow for sustainable development.


Introduction
With the evolution and rapid development of human society, the ecological environment of the earth has been destroyed to varying degrees in various countries, and a common task facing mankind is how to effectively solve the problem of greenhouse effect.With the concept of "peak carbon dioxide emissions, carbon neutrality" put forward, human beings have deeply realized the importance and great significance of developing a low-carbon economy.Promoting a comprehensive green transformation of economic and social development and building a harmonious coexistence between man and nature are the common vision of human beings to control global climate change and ecological transformation of human civilization [1].
The term "low-carbon economy" first appeared in the white paper "Our Future Energy: Creating a Low-carbon Economy" published by the British government in February 2003.The low-carbon economy has now become the focus of global attention and one of the major hot issues in academic research [2].With regard to the connotation of low-carbon economy, Chen Shi, a pair of scholars, pointed out that low-carbon economy is an economic form with a certain level of carbon productivity and human development, and its main purpose is to control greenhouse gas emissions, emphasizing that the world should move towards common prosperity on the premise of protecting the ecological environment and environmental climate [3].Zhang Xiufan believes that the transformation of low-carbon economy aims at carbon emission reduction, and the optimization of industrial structure, the change of industrial organization mode, and the transformation of economic development mode and system are important contents [4].Wu Caixia and Lv Zhichen aim at building and developing a low-carbon city, and research shows that the economic development of low-carbon cities is a multi-dimensional complex system including society, economy, population, resources and environment [5,6].
In the research on the coordinated development of low-carbon economy and society, Zhou Li and others believe that the synergistic benefits generated by the development of low-carbon economy can offset some welfare losses in the process of achieving emission reduction targets, thus providing shortcuts for achieving low-carbon economic goals [7].Jia Lifang's research emphasizes the need to analyze the system structure for realizing the transformation and development of a low-carbon economy based on each country's national conditions."This analysis should encompass technology, market, and governance.Key areas include adjusting the mode and structure of economic development, developing low-carbon technologies, and optimizing the energy structure, all guiding coordinated development of the low-carbon economy and the overall economy and society [8].Judging from the existing scholars' research results, the connotation and coordinated development mode of the low-carbon economy have become more mature.However, there are relatively few studies on the construction of a comprehensive evaluation index system for the low-carbon economic development level and the measurement of this level in different countries.This paper focuses on the United States, China, Japan, Germany, and Britain, the top five in the world GDP for 2022, as the research objects.It constructs a comprehensive evaluation index system for the development level of the low-carbon economy, measures the weight of each index using the TOPSIS evaluation method with entropy weight and the grey relational model.The paper evaluates the development level of the low-carbon economy in these five countries and offers suggestions and paths to promote its development based on the measurement and evaluation results.This aims to provide valuable reference for the positive development of low-carbon economies in various countries.The innovations of this paper are as follows: first, compared with other research results, a comprehensive evaluation index system for measuring the development level of lowcarbon economy is constructed more comprehensively and scientifically, and countries all over the world can use this set of measurement indicators for comprehensive evaluation according to their own data to understand their own development level of low-carbon economy; Second, according to the measurement results, it is proposed to strengthen the government's guidance and support for the development of low-carbon economy and advocate the low-carbon consumption lifestyle of residents; Accelerate the adjustment of industrial structure and vigorously develop low-carbon industries; The three measures of accelerating technological innovation and actively exploring the development of new energy can be used for reference by all countries in the world.

Selection of evaluation indicators and construction of comprehensive evaluation system for urban low-carbon economic development level
When selecting the evaluation indicators of urban low-carbon economic development level, it's essential to aim for a comprehensive and objective assessment.This can be achieved through the creation of a scientifically sound and comprehensive evaluation index system, ensuring the collection of evaluation indicators is comprehensive and objective.It is mainly divided into two stages.In the literature review stage, the indicators that scholars think are more mature to measure the development level of urban low-carbon economy are collected and sorted, and a preliminary comprehensive evaluation index system is constructed.The second stage is to conduct on-the-spot investigation and interview on the preliminary evaluation indicators, so as to obtain a more scientific and complete comprehensive evaluation index system for evaluating the development level of low-carbon economy in cities.
In the first stage, the focus is on sorting out the literature achievements of existing scholars concerning the measurement and comprehensive evaluation of low-carbon economy development level.The process involves selecting more mature evaluation indicators from these existing research achievements to serve as the basic indicators for evaluating the development level of low-carbon economy in cities. Judging from the achievements of current scholars' research, since 2010, more and more scholars at home and abroad have devoted themselves to the research of low-carbon economy and achieved phased research results.Li Tao highlighted the assessment of urban low-carbon economic development by taking into account emission intensity of pollutants like carbon dioxide and sulfur dioxide, as well as factors like energy structure and per capita GDP." "In the choice of assessment indicators for urban low-carbon economic development, Li Tao stressed the evaluation of emission intensity of pollutants such as carbon dioxide and sulfur dioxide.Furthermore, attention was given to factors such as energy structure and per capita GDP [9].
Wei Hua and others believe that the evaluation index of urban low-carbon economic development level should include four dimensions: economy and technology, energy emission, social development, resources and environment [10].Xie Zhixiang and other studies have pointed out that energy consumption, green space coverage and car ownership are important indicators to evaluate the development of low-carbon economy in cities [11].Li Min and others built an evaluation index system for the development of low-carbon economy.The research shows that the coverage rate of urban green space, the proportion of tertiary industry, the number of days with good air in a year, and the energy consumption per 10,000 yuan of GDP are effective indicators for evaluating the development level of low-carbon economy in cities [12].According to the characteristics of low-carbon economy, Li Mingsheng and others selected energy consumption, carbon emissions and per capita GDP as important indicators to measure the development level of low-carbon economy [13].
On the other hand, in the study of influencing factors of urban low-carbon economic development, Shi Xuefei and other studies believe that the level of low-carbon environment, low-carbon industry and residents' living standards are the main influencing factors of Tianjin's low-carbon economic development [14].Liu Xiaohui and others adopted the revised TOPSIS method to build a low-carbon economy evaluation model, and the research pointed out that the energy consumption of industrial enterprises above designated size, the smoke and dust emissions of 10,000 yuan GDP, and disposable income of urban households are important factors affecting the development of urban low-carbon economy [15].Zhang Lihua and others studied the symbiotic relationship between port economy and low-carbon economy in coastal cities, and pointed out that industrial waste utilization rate, per capita green space area, carbon emissions per 10,000 yuan GDP, Engel coefficient, energy consumption per unit GDP and so on are important factors that affect the development level of low-carbon economy [16].
Combing the research results of scholars on comprehensive evaluation of the development level of low-carbon economy, 11 indicators, such as per capita GDP, per capita disposable income, the proportion of tertiary industry in GDP, per capita green space area, environmental financial expenditure, days with excellent urban air quality, CO 2 emission per unit GDP, energy consumption per unit GDP, comprehensive utilization rate of industrial solid waste, Engel coefficient and harmless treatment rate of domestic garbage, were preliminarily selected as the evaluation level of urban low-carbon economy.
In the second stage, the index system for comprehensively assessing urban low-carbon economic development, constructed in the first stage through literature review, is a key focus.Three experts and scholars with extensive experience in low-carbon economy and ecological environment protection, both domestically and internationally, are selected for participation.Additionally, two individuals with prolonged engagement in the government department of the Ecological Environment Protection and Development and Reform Commission, specializing in environmental and economic development management, are included in the group through brainstorming.The measurement indicators and influencing factors for evaluating the development level of urban low-carbon economy are put forward.After finishing, it is found that about 70% of the indicators mentioned are the same as or similar to those obtained by literature review.Secondly, we will inform the experts who brainstorm about the indicators obtained from literature combing, and compare, supplement and optimize the indicators for evaluating the development level of low-carbon economy in cities.Finally, it is determined to evaluate the development level of urban low-carbon economy from four dimensions: urban economic development level, environmental quality, energy consumption emission intensity and social development speed, and 15 indicators, such as per capita GDP, per capita disposable income and per capita green space area.See Table 1 for details.

Urban low-carbon economic development level evaluation model construction and data collection
According to the comprehensive evaluation index system of urban low-carbon economic development level, five countries including China, the United States, Japan, Britain and Germany are selected from all over the world for comprehensive evaluation, and the current status and level of low-carbon economic development in these five countries are analyzed, so as to explore effective ways and methods to improve the quality and ability of low-carbon economic development, and provide ideas and reference for low-carbon economic development in other countries in the world, so as to promote the development of low-carbon life in the global economy.

Model construction and implementation principle
The TOPSIS evaluation method of entropy weight can judge the advantages and disadvantages of the schemes and rank the survey samples.Its basic principle is to measure the actual development level of the schemes to be selected or the research objects by calculating the Euclidean distance between the schemes to be selected and the ideal schemes.The TOPSIS evaluation method with entropy weight has low requirements on the data collected by survey samples, which is convenient for measurement and calculation, and can reflect the advantages and disadvantages of each scheme and the ranking of schemes through measurement, so it is widely used in many practical problems of scheme selection and ranking.
However, the main defect of this method is that it only uses Euclidean distance as the criterion to judge the advantages and disadvantages of the scheme, and it cannot fully reflect the dynamic changes of the data sequence of the sample or the research object, which is complementary to the grey relational analysis.Although the grey relational analysis method can reflect the advantages and disadvantages of the sample or the investigated object from the dynamic curve of the data, it cannot directly reflect the distance position of the sample [17][18][19].Based on the advantages and disadvantages of TOPSIS evaluation method and grey relational analysis method based on entropy weight, through literature review and practical verification and analysis, the author thinks that grey relational analysis method can effectively make up for the shortcomings of entropy weight method, and combine the two research methods to evaluate the development level of the system better and more accurately, and make a more scientific choice and ranking of evaluation schemes and evaluation objects, which is also a method choice and innovation different from other research results.
According to the TOPSIS evaluation method principle of entropy weight, the development level of urban low-carbon economy is comprehensively evaluated, and the following measurement model is constructed.P in the comprehensive evaluation model of urban low-carbon economic development level represents the object to be measured or evaluated, and the evaluation index set is composed of Q measurement indicators, thus forming an index data matrix.As there are both positive indicators and negative indicators in the 15 indicators for the comprehensive evaluation of urban low-carbon economic development level, the collected data can be standardized by the mean method.The standardized processing method is to compare the statistical value of each indicator of each enterprise sample data with the mean value of all corresponding indicators of all enterprises (Formula 1) to get the standardized matrix A.
In Formula 1, the I-th sample data is X i ¼ ðx i ð1Þ; x i ð2Þ; � � � ; x i ðqÞÞði ¼ 1; 2; � � � ; pÞ 3.1.1.Entropy weight processing of standardized matrix.Firstly, the entropy weight of each index is calculated.Calculate the index proportion, index entropy value and index difference coefficient of the standardized data, and finally get the weight of each index (Formula 2 to Formula 5): Secondly, calculate the weight set c of the normalized matrix (Eq 6): Relative closeness based on Euclidean distance.First, the positive ideal solution and the negative ideal solution are determined.The specific method is to find out the optimal value and the worst value of 15 indicators from P digital transformation measurement objects, and then combine these values into positive ideal solutions and negative ideal solutions respectively, as follows: Positive ideal solution: Negative ideal solution: Secondly, from the weight set B of the standardized matrix, calculate the distance from the development level of low-carbon economy in cities of P countries to the ideal solution (Eq 7): ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi Calculate the distance from the development level of urban low-carbon economy to the negative ideal solution (Eq 8): ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi Finally, calculate the relative closeness of Euclidean distance (Eq 9): Relative closeness based on grey correlation.First, calculate the absolute difference.The absolute difference between each sample enterprise index and the ideal scheme index should be calculated, that is jx 0 ðkÞ À x i ðkÞj.On the basis of calculating the absolute difference, the maximum difference between two poles max p i¼1 max q i¼1 jx 0 ðkÞ À x i ðkÞj and the minimum difference between two stages min p i¼1 min q i¼1 jx 0 ðkÞ À x i ðkÞj are calculated.Secondly, calculate the correlation coefficient.The correlation coefficient between each sample country and the indicators corresponding to the positive ideal solution and the negative ideal solution shall be calculated (Eq 10):

Formula10
In Formula 10, ρ is the resolution coefficient, and the value range is (0,1).Generally speaking, the smaller the value of ρ, the greater the difference between correlation coefficients and the stronger the discrimination ability.Usually, the value of ρ is 0.5.
Finally, the relative closeness based on grey correlation is calculated.First, calculate the degree of correlation H þ i and negative degree of correlation H À i between the i-th country and the positive ideal solution, and then calculate the relative closeness H * i of grey correlation (Eqs 11 to 13). 1.Because the calculation scales of Euclidean distance and grey correlation degree are different, it is not possible to combine them directly, so it must be dimensionless first.L i in Formula 14 represents 2. Euclidean distance represents the distance between the evaluation sample and the ideal solution, so the greater the value of D ? 0À i , the closer it is to the positive ideal solution; The grey correlation degree indicates the correlation degree between the evaluation sample and the ideal solution, so the greater the value of H ? 0 þ i , the closer it is to the positive ideal solution.Therefore, the combination should be carried out according to the following Formula 15 and Formula 16, in which R þ i represents the closeness between the sample of the measure and the positive ideal solution, and R À i represents the closeness between the sample of the measure and the negative ideal solution.
In Formula 15 and Formula 16, α and β represent the evaluators' preference for Euclidean distance and gray correlation degree, and the sum of them is 1.In the comprehensive evaluation of urban low-carbon economic development level, the values of α and β are both 0.5, which means that Euclidean distance and gray correlation degree are of the same importance in measuring urban low-carbon economic development level.3. Calculate the relative closeness degree R * i between the measured sample and the ideal solution (Formula 17), which is used to comprehensively reflect the development level of lowcarbon economy in cities of different countries, and rank them in descending order, and analyze the final results.

Data acquisition and analysis
In As can be seen from Table 2, the minimum values of standardized statistical data are all 0, and the maximum values are all 1; Judging from the average and standard deviation of 15 indicators, the overall dispersion degree of data is not high, and the evaluation value is relatively concentrated.To some extent, it reflects that the index system for evaluating the development level of urban low-carbon economy is scientific and reasonable, and it can accurately measure the development level of urban low-carbon economy.

Reliability and Validity Test.
1. Reliability test.Cronbach method is used to test the reliability of statistical data.With the help of SPSS(version22), the Cronbach coefficient is tested (as shown in Table 3).
Table 3 shows that the overall reliability coefficient of the comprehensive evaluation index system of urban low-carbon economic development level is 0.824, indicating that the obtained data has good reliability.

Validity analysis. With the help of SPSS (version 22
), the validity of statistical data is analyzed by exploratory factor analysis.After inspection, KMO value is 0.786, and Bartlett spherical test value is 198.234, as shown in Table 4. From this, it can be judged that the evaluation index system designed by the research has good structural validity and strong explanatory power to measure the development level of urban low-carbon economy.The overall result of the above data test shows that the comprehensive evaluation index of urban low-carbon economic development level has passed the test of reliability and validity, which means that the evaluation system of urban low-carbon economic development level is scientific and reasonable, and the reliability and quality of the obtained statistical data are high, and the structural validity is good, which can support the follow-up research work of comprehensive evaluation of urban low-carbon economic development level.

4.Evaluation and result analysis of the development level of lowcarbon economy in cities
According to the comprehensive evaluation model and evaluation index system of urban lowcarbon economic development level, this paper explores the importance of evaluation index in measuring the development level of urban low-carbon economy by using TOPSIS evaluation method of entropy weight and grey relational model, and evaluates the development level of low-carbon economy in five countries, laying a foundation for promoting the promotion path of urban low-carbon economic development level.

Comprehensive measurement of urban low-carbon economic development level
On the basis of the reliability and validity test of the collected data, the entropy weight TOPSIS model and grey relational analysis are used to measure the scores of 15 indicators in five countries, including China, the United States, Japan, Britain and Germany.Firstly, 15 index data of five countries are standardized, and the entropy weight after standardization is calculated.
For the standardized data, the index difference coefficient g(k) is calculated, and finally the weight W(k) of each index is obtained, where k is from 1 to 15, that is, the sum of 15 index difference coefficients is divided by the index difference coefficient of each index.
Secondly, calculate the relative closeness of Euclidean distance.
Find out the optimal values and the worst values of 15 indicators from the evaluation objects of five countries, such as China, the United States, Japan, Britain and Germany, and form positive ideal solutions and negative ideal solutions respectively.Calculate the distance Calculate the correlation degree H þ i and negative correlation degree H À i between the first evaluation index and the positive ideal solution, and then calculate the relative closeness degree H * i of grey correlation.Finally, the relative closeness R * i between the evaluation sample and the ideal solution is calculated.
In the formula, R þ i represents the closeness between the evaluated sample and the positive ideal solution, and R À i represents the closeness between the evaluated sample and the negative ideal solution.R * i is used to comprehensively reflect the entropy value of evaluation index of urban low-carbon economic development level, and the results are shown in Table 5.
From the TOPSIS model of entropy weight method and the results of grey relational analysis, it can be seen that among the 15 indicators for measuring the development level of urban low-carbon economy, the importance of three indicators, such as the amount of financial allocation for environmental protection, the number of civil cars owned by five countries and the amount of CO2 emitted per unit of GDP, ranks first, second and third respectively, which means that these three indicators play a significant role in promoting the development of urban low-carbon economy; Seven indicators, such as per capita housing area, Engel coefficient, per capita green area, comprehensive utilization rate of industrial solid waste, proportion of green coverage area, energy consumption per unit GDP and compliance rate of industrial wastewater discharge, play an obvious role in promoting the development of urban low-carbon economy; The harmless treatment rate of domestic garbage, the proportion of days with good air quality in the whole year, per capita disposable income, per capita GDP and the proportion of tertiary industry in GDP have certain effects on promoting the development of low-carbon economy in cities.The 15 comprehensive evaluation indexes are divided into three echelons according to their remarkable, obvious and general effects on promoting the development of urban low-carbon economy, as shown in Table 6.

Analysis of comprehensive evaluation results of urban low-carbon economic development level
According to the comprehensive evaluation index system of urban low-carbon economic development level, combined with the measurement weights of each index, this paper measures and evaluates the overall urban low-carbon economic development level of China, the United States, Japan, Britain and Germany, and understands the current situation of urban low-carbon economic development in China, providing reference and basis for the government to plan the development strategy of low-carbon economy and formulate measures to develop low-carbon economy.The social science statistical analysis software SPSS(version22) is used to analyze the factors of 15 evaluation indexes, explore public factors, and measure and rank the development status of low-carbon economy in five countries, as shown in Tables 7  and 8. Judging from the comprehensive evaluation scores of low-carbon economic development levels in China, the United States, Japan, Britain and Germany, the overall situation of low-

Ways to improve the development level of urban low-carbon economy
The above research results show that the comprehensive evaluation index system of urban low-carbon economic development level constructed from four dimensions: economic development level, environmental quality, energy consumption emission intensity and social development speed is more comprehensive and scientific, and can objectively and effectively measure the current level of low-carbon economic development in all countries of the world; The contribution of 15 evaluation indicators to the overall goal is divided into three echelons: significant, obvious and general, and countries can effectively propose effective ways to reduce carbon emissions; According to the measurement results, except for the United States, which meets the development standard of low-carbon economy, the other four countries are all medium-carbon economies, and there is a big difference.According to the importance and evaluation results of comprehensive evaluation index of urban low-carbon economic development level, combined with the economic development reality of five countries, this paper puts forward suggestions and paths to promote the development of low-carbon economy from the following three aspects, providing reference for the good development of low-carbon economy in various countries.First, increase the government's efforts to guide and support the development of low-carbon economy and advocate residents' low-carbon consumption lifestyle.In the comprehensive evaluation index of the development level of urban low-carbon economy, the most important factor is the government's financial expenditure on environmental protection, that is, governments should attach importance to the protection of the ecological environment, increase financial expenditure, expand the coverage area of urban green space, improve the harmless treatment rate of domestic garbage, standardize the guidance and cultivation of residents' low-carbon lifestyle through laws and systems, advocate the green travel mode of urban residents, and promote walking, cycling and public transportation.Adhere to the concept that houses are used for living, not for speculation, and reduce the per capita housing area.Firmly establish the Lucid waters and lush mountains are invaluable assets concept, protect the ecological environment, and build a beautiful picture of harmonious coexistence and sustainable development between man and nature.Second, accelerate the adjustment of industrial structure and vigorously develop low-carbon industries.Judging from the development history and economic development mode of the five countries, most of the industrial economic development has experienced high pollution and high consumption stages.According to the comprehensive index results of low-carbon economic evaluation, we will speed up the adjustment, transformation and upgrading of industrial structure, eliminate or transform and upgrade backward industries such as iron and steel industry, traditional metallurgy, thermal power generation, and urban pollution, and vigorously develop tertiary industries such as finance, tourism, and modern service industry.It can reduce CO 2 emission per unit GDP and energy consumption per unit GDP, improve the comprehensive utilization rate of industrial solid waste, increase the number of clean energy vehicles, reduce the number of civilian vehicles that consume oil, and effectively promote the development of urban low-carbon economy.
Third, speed up technological innovation and actively explore and develop new energy sources.Judging from the energy use structure of five countries, although the proportion of energy such as wind energy, solar energy and bioenergy has increased, the main energy sources in the world today are still coal, oil and natural gas.The extensive use of these three kinds of energy sources has seriously affected and destroyed the ecological environment.The greenhouse effect has caused global warming, and a large amount of sulfur dioxide has been discharged to form acid rain, which has seriously affected and threatened the development of low-carbon economy.Therefore, all countries in the world should actively accelerate technological innovation, explore new and clean energy sources such as combustible ice, nuclear energy, geothermal energy and tidal energy, and constantly improve the utilization efficiency of solar energy, wind energy and bioenergy, so as to make cities bluer in sky, cleaner in water and higher in air quality, and the development level and quality of urban low-carbon economy are higher and better.
Taking the road of low-carbon economic development, protecting the ecological balance and sustainable development of the earth is a basic national policy that all countries in the world should pay close attention to.The limitation of this paper is that the number of selected countries is relatively small.In the follow-up study, the comprehensive evaluation of low-carbon economic development will be extended to more countries, so as to grasp the development level of low-carbon economy in all countries, explore more ways to effectively reduce carbon emissions, and promote the green and sustainable development of the world economy.

. 1 . 4 .
Relative closeness between TOPSIS evaluation method based on entropy weight and grey relational model.

Table 1 . Comprehensive evaluation index system of urban low-carbon economic development level.
https://doi.org/10.1371/journal.pone.0299688.t001 terms of data acquisition, according to the 15 secondary indicators of the comprehensive evaluation system of urban low-carbon economic development level, by consulting World Statistical Yearbook 2022, United Nations Statistical Yearbook 2022, Global Times Data, World Engel Coefficient, Global Air Quality Report 2022 and statistical yearbooks of China, the United States, Japan, Britain and Germany, 15 comprehensive indicators of urban low-carbon economic development level in 2022 in five countries were obtained.3.2.1 Descriptive statistics of data.SPSS (version22) was used to make descriptive statistical analysis on the data of 15 comprehensive evaluation indicators of urban low-carbon development level in five countries, and the results are shown in Table 2.

Table 2 . Descriptive statistics of comprehensive evaluation index data of urban low-carbon development level. Evaluating indicator N minimum value maximum average number Standard deviation
https://doi.org/10.1371/journal.pone.0299688.t002

Table 4 . KMO and Bartlett test.
from the positive ideal solution to the negative ideal solution of the development level of low-carbon economy in five countries, calculate the relative closeness D À i of Euclidean distance, and calculate the relative closeness D * i of grey correlation.

Table 7 . Analysis results of comprehensive evaluation factors of urban low-carbon economic development level. Evaluating indicator Initial eigenvalue The obtained sum of squares is loaded.
American cities is good, and according to the evaluation standards of low-carbon economic development levels, American cities have reached the development standards of low-carbon economy; Followed by Germany and Japan, among the five countries, the comprehensive evaluation of urban low-carbon economic development level ranks second and third, which is a low-carbon economy country; The comprehensive evaluation of the development level of low-carbon economy in British cities ranks fourth.Although it belongs to the national sequence of low-carbon economy, there is still a certain gap between it and Germany and Japan.China ranks last in the development of low-carbon economy in five cities, and there is still a big gap with the other four countries in terms of measurement scores.Judging from the evaluation criteria of low-carbon economic development level, it belongs to a medium-carbon economy country, and there is still a long way to go on the road of low-carbon economic development.Compared with other research results, the conclusion of this study has more important practical value, and the development level and gap of low-carbon economy in five countries are more accurately defined from the quantitative point of view.It makes the five countries clear their own measurement scores, measures to be taken in promoting the development of low-carbon economy and shortcomings from each evaluation index, and the conclusion is more innovative and practical.